A solution to a linear integral equation with an application to statistics of infinitely divisible moving averages

摘要

Abstract For a stationary moving average random field, a nonparametric low frequency estimator of the Lévy density of its infinitely divisible independently scattered integrator measure is given. The plug‐in estimate is based on the solution w of the linear integral equation v(x)=∫?dg(s)w(h(s)x)ds, where g,h:?d→? are given measurable functions and v is a (weighted) L2‐function on ?. We investigate conditions for the existence and uniqueness of this solution and give L2‐error bounds for the resulting estimates. An application to pure jump moving averages and a simulation study round off the paper.